Some results for the compound Poisson process that is perturbed by diffusion. (English) Zbl 1004.60014
The surplus processes perturbed by diffusion are considered. The subject of the distributions of the surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation and ruin caused by a claim are studied. Some joint distribution densities are obtained by using the techniques from martingale theory and renewal theory.
Reviewer: Chun Su (Hefei)
MSC:
| 60E15 | Inequalities; stochastic orderings |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
compound Poisson process; diffusion; ruin probabilities; oscillation; claim; surplus; joint distributionReferences:
| [1] | Dickson, D.C.M. On the Distribution of the Surplus Prior to Ruin. Insurance: Mathematics and Economics, 1992, 11: 191–207 · Zbl 0770.62090 · doi:10.1016/0167-6687(92)90026-8 |
| [2] | Dufresne, F., Gerber, H.U. The Surpluses Immediately before and at Ruin, and the Amount of the Claim Causing Ruin. Insurance: Mathematics and Economics, 1988, 7: 193–199 · Zbl 0674.62072 · doi:10.1016/0167-6687(88)90076-5 |
| [3] | Dufresne, F., Gerber, H.U. Risk Theory for the Compound Poisson Process that is Perturbed by Diffusion. Insurance: Mathematics and Economics, 1991, 10: 51–59 · Zbl 0723.62065 · doi:10.1016/0167-6687(91)90023-Q |
| [4] | Schäl, M. On Hitting Times for Jump-diffusion Processes with Past Dependent Local Characteristics. Stochastic Processes and their Applications, 1993, 47: 131–142 · Zbl 0802.60039 · doi:10.1016/0304-4149(93)90099-P |
| [5] | Wang, G.L., Wu R. Some Distributions for Classical Risk Process that is Perturbed by Diffusion. Insurance: Mathematics and Economics, 2000, 26: 15–24 · Zbl 0961.62095 · doi:10.1016/S0167-6687(99)00035-9 |
| [6] | Zhang, C.S., Wu R. On the Distributions of the Surplus of the D-E Model Prior to and at Ruin. Insurance: Mathematics and Economics, 1999, 24: 309–321 · Zbl 0963.91063 · doi:10.1016/S0167-6687(99)00005-0 |
| [7] | Zhang, C.S., Wu R. A Note for the Probabilities of Ruin with Differentiabilities. Chinese Journal of Applied and Statistics, 2001, 17(3): 267–275 · Zbl 1155.62471 |
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